{
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  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Exercícios\n",
    "\n",
    "1 - Aplique os algoritmos K-means [1] e AgglomerativeClustering [2] em qualquer dataset que você desejar (recomendação: iris). Compare os resultados utilizando métricas de avaliação de clusteres (completeness e homogeneity, por exemplo) [3].\n",
    "\n",
    "* [1] http://scikit-learn.org/stable/modules/clustering.html#k-means\n",
    "\n",
    "* [2] http://scikit-learn.org/0.17/modules/clustering.html#hierarchical-clustering\n",
    "\n",
    "* [3] http://scikit-learn.org/stable/modules/clustering.html#clustering-evaluation\n",
    "\n",
    "2 - Qual o valor de K (número de clusteres) você escolheu para a questão anterior? Desenvolva o Método do Cotovelo (não utilizar lib!) e descubra o K mais adequado. Após descobrir, aplique novamente o K-means com o K adequado. \n",
    "\n",
    "* Ajuda: atributos do [k-means](http://scikit-learn.org/0.17/modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans)\n",
    "\n",
    "3 - Após a questão 2, você aplicou o algoritmo com K apropriado. Refaça o cálculo das métricas de acordo com os resultados de clusters obtidos com a questão anterior e verifique se o resultado melhorou.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Parte 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Bibliotecas\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import normalize\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
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       "     0    1    2    3\n",
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     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "#Carrega o dataset iris\n",
    "iris = datasets.load_iris()\n",
    "df = pd.DataFrame(iris.data)\n",
    "y = iris.target\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
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    {
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   "source": [
    "#Normaliza as features antes de aplicar PCA\n",
    "norm = normalize(df)/2\n",
    "df = pd.DataFrame(norm)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
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04A3gPKALcIUQonjD801AlpSyHfAK8FzB9gPAhVLK7sB1wMcVLc/RklIiQ6uRgV+RVmbp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\nUaw4GGOMiWLFwRhjTBQrDsYYY6L8PzntX69ARRtCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2594a0ab630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Aplica PCA para duas dimensões\n",
    "df_pca = PCA(n_components=2).fit_transform(df)\n",
    "\n",
    "#Plota os dados em duas dimensões\n",
    "fig,ax = plt.subplots()\n",
    "ax.scatter(df_pca[:,0], df_pca[:,1], c=y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "# KMeans clustering\n",
    "km = KMeans(n_clusters=3)\n",
    "km.fit(df_pca)\n",
    "clusters = km.predict(df_pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NTLlv3jWezSu24s8PEPSHCOQH2LJqG2/c+f7Rf5PViAoOCSRSxmK/rhHgm4As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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25945f9c668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plota os dados em duas dimensões após kmeans\n",
    "fig,ax = plt.subplots()\n",
    "ax.scatter(df_pca[:,0], df_pca[:,1], c=clusters)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "homogeneity = 0.8983263672602775\n",
      "completeness = 0.9010648908640206\n"
     ]
    }
   ],
   "source": [
    "#Utilizar métricas de avaliação de clusteres (completeness e homogeneity)\n",
    "score_homo = metrics.homogeneity_score(y,clusters)\n",
    "score_comp = metrics.completeness_score(y,clusters) \n",
    "\n",
    "print('homogeneity = {0}'.format(score_homo))\n",
    "print('completeness = {0}'.format(score_comp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parte 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x25949756cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Elbows method\n",
    "clusters_result = []\n",
    "for i in range(9):\n",
    "    km = KMeans(n_clusters=i+1)\n",
    "    km.fit(df_pca)   \n",
    "    clusters_result.append(km.inertia_)\n",
    "    \n",
    "# Plotagens\n",
    "plt.figure()\n",
    "plt.plot(np.arange(1,10),clusters_result,'ro-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Z+63hmEdBSSl56/4PcWW4s/JEed0+0pLSmTzy6zOuVynZpPQjE+6DtJf1b/me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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2594b26d828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# KMeans clustering\n",
    "km = KMeans(n_clusters=2)\n",
    "km.fit(df_pca)\n",
    "clusters = km.predict(df_pca)\n",
    "\n",
    "#Plota os dados em duas dimensões\n",
    "fig,ax = plt.subplots()\n",
    "ax.scatter(df_pca[:,0], df_pca[:,1], c=clusters)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parte 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "homogeneity = 0.5793801642856945\n",
      "completeness = 0.9999999999999997\n"
     ]
    }
   ],
   "source": [
    "#Utilizar métricas de avaliação de clusteres (completeness e homogeneity)\n",
    "score_homo = metrics.homogeneity_score(y,clusters)\n",
    "score_comp = metrics.completeness_score(y,clusters) \n",
    "\n",
    "print('homogeneity = {0}'.format(score_homo))\n",
    "print('completeness = {0}'.format(score_comp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusão"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para algoritmos de clusterização, o conhecimento sobre os dados é muito importante. Reduzindo as features para 2 componentes, através do PCA, deu para visualizar as classes e observar que uma classe é linearmente separável e as outras duas não. Com o conhecimento prévio, sobre o número de classes do dataset do iris. O kmeans com k = 3 deu um bom resultado, quando utilizado a euristica do método do cotovelo, o indicado foi usar duas classes, de acordo com a distância aos centroides, porém o resultado ficou pior. Indicando que o K = 3 é realmente uma boa escolha. Para este caso o método do cotovelo falhou, por causa da distribuição dos dados e isso foi em decorrência da normalização combinada com o PCA. Talvez com o uso de mais features, ou a utilização de outro tipo de normalização, a euristica funcionaria corretamente. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
